Design and study of mixed animal-robot societies are the fields of scientific exploration that can bring new opportunities for research into the group behavior of social animals. Our goal is to develop a Chicken Robot – an autonomous mobile robot, socially acceptable by a group of chicks and able to interact with them using appropriate communication channels. One of the basic requirements to such a robot is the safety of its motion with respect to the chicks, so it has to be endowed with an efficient real-time collision avoidance system. In this paper we present a fuzzy obstacle avoidance system that was designed for the Chicken Robot using the theory of fuzzy relation equations. This approach allows to easily check a consistency of a used rule base and provides a more systematic approach to design of fuzzy control systems comparing with the classical techniques. The experimental results demonstrate that a mobile robot equipped with the presented system is able to successfully avoid obstacles and safely navigate on an experimental arena.